This paper deals with the steady-state waiting time distribution in the GI/GI/1/k {GI/GI/1 with k waiting places) queue. Marshall[8]'s generalized Pollaczek-Khinchine formula is generalized to the GI/GI/1/k model. From the resulting formulas, we obtain approximation formulas for the waiting time distribution and for the probabilities of the system being empty and of customer loss. The quality of those approximations is shown by numerical examples.
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Masakiyo Miyazawa (1987) studied this question.
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